Modern trends in Operator Theory and Geometric Analysis

Contribution List

11. Analysis on surfaces with bounded integral curvature

Batu Güneysu (Christian-Albrechts-Universität zu Kiel)

The class of metric surfaces of bounded integral curvature (BIC) is a large class of singular surfaces including e.g. the class of polyhedral surfaces. These surfaces have just enough regularity to define the curvature as a signed Radon measure, and compact BIC surfaces
admit a natural Gauss-Bonnet Theorem. Given a complete surface of bounded integral curvature (without cusps), together with...

16. Extracting subcomplexes on Carnot groups

Francesca Tripaldi (University of Leeds)

Differential complexes are fundamental tools in geometry and analysis, encoding geometric structures through differential operators and cohomological invariants. In subRiemannian geometry, the classical de Rham complex is often replaced by more intrinsic subcomplexes, such as the Rumin complex, which better reflect the underlying graded structure. In this talk, I will discuss the problem of...

14. Extrema of functional determinants on orthogonal tori

Julie Marie Rowlett (Chalmers University of Technology)

The search for extrema is a central theme in both mathematics and physics. In this talk, we address the following question: among all n-dimensional orthogonal tori of unit volume, which one maximizes the determinant of the Laplacian? This determinant is obtained via the zeta regularization method, originally introduced by Ray and Singer to define an analytic analogue of the topological...

6. Integral and spectral curvature condition in dimension 3

Gilles Carron (Nantes Université)

I will discuss of various curvature or spectral constraints implying that a complete Riemannian manifold of dimension 3 is diffeomorphic to the Euclidean space. I will also provide some recent topological finiteness result obtained in collaboration with Dorian Martino (ETH Zürich).

10. Leibenson's equation on Riemannian manifolds

Alexander Grigor’yan (Universität Bielefeld)

15. Magnetic Laplacian and the conformal class of a surface

Alessandro Savo (Sapienza Università di Roma)

On a closed Riemannian surface we study the magnetic Laplacian with magnetic potential given by a harmonic 1-form A. Its lowest eigenvalue (magnetic ground state energy) is positive, unless A represents an integral cohomology class. We isolate a countable set of ground state energies which we call ''ground state spectrum'' of the metric. Our main result is to show that the ground state...

18. Stable hypersurfaces: rigidity and topology at infinity.

Claudia Pontuale (Università degli Studi dell’Aquila)

We discuss rigidity phenomena for complete, noncompact, stable hypersurfaces with constant mean curvature, with particular emphasis on questions related to Do Carmo’s problem. We will review some classical results and then consider extensions to the anisotropic setting, focusing on how stability can constrain the global geometry and topology at infinity. Some recent results and open questions...

7. TBA

Alberto Enciso (Instituto de Ciencias Matemáticas)

8. TBA

Albachiara Cogo (Scuola Normale Superiore)

9. TBA

Sara Farinelli (Università di Genova)

17. TBA

Lorenzo Maniscalco (Università di Torino)

19. TBA

Luca Benatti (University of Vienna)

20. TBA

Simone Vincini (Universität Wien)

21. TBA

Davide Carazzato (Universität Wien)

13. The nodal length of random spherical harmonics

Maurizia Rossi (Università degli Studi di Milano-Bicocca)

In this talk we investigate the behavior of the "typical" Laplacian eigenfunction of a compact smooth Riemannian manifold. In particular, motivated by both Yau's conjecture on nodal sets and Berry's ansatz on planar random waves, we consider Gaussian eigenfunctions on the sphere and study the distribution of the length of their nodal lines in the high energy limit. This result raises several...